Phase-space rotations and orbital Stokes parameters

We introduce the orbital Stokes parameters as a linear combination of a beam's second-order moments. Similar to the ones describing the field polarization and associated with beam energy and its spin angular momentum, the orbital Stokes parameters are related to the total beam width and its orbital angular momentum. We derive the transformation laws for these parameters during beam propagation through first-order optical systems associated with phase-space rotations. The values of the orbital Stokes parameters for Gaussian modes and arbitrary fields expressed as their linear superposition are obtained

Signal representation on the angular Poincare sphere, based on second-order moments

Based on the analysis of second-order moments, a generalized canonical representation of a two-dimensional optical signal is proposed, which is associated with the angular Poincare sphere. Vortex-free ( or zero-twist) optical beams arise on the equator of this sphere, while beams with a maximum vorticity ( or maximum twist) are located at the poles. An easy way is shown how the latitude on the sphere, which is a measure for the degree of vorticity, can be derived from the second-order moments. The latitude is invariant when the beam propagates through a first-order optical system between conjugate planes. To change the vorticity of a beam, a system that does not operate between conjugate planes is needed, with the gyrator as the prime representative of such a system. A direct way is derived to find an optical system ( consisting of a lens, a magnifier, a rotator, and a gyrator) that transforms a beam with an arbitrary moment matrix into its canonical form

Characterization of host tolerance to Striga hermonthica

One of the most promising control options against the parasitic weed Striga hermonthica is the use of crop varieties that combine resistance with high levels of tolerance. The aim of this study was to clarify the relation between Striga infestation level, Striga infection level and relative yield loss of sorghum and to use this insight for exploring the options for a proper screening procedure for tolerance. In three pot experiments, conducted in Mali (2003) and The Netherlands (2003, 2004), four sorghum genotypes were exposed to a range of Striga infestation levels, ranging from 0.0625 to 16 seeds cm−3. Observations included regular Striga emergence counts and sorghum grain yield at maturity. There were significant genotype, infestation and genotype × infestation effects on sorghum yield. The relation between infestation level and infection level was density dependent. Furthermore, the relation between Striga infection level and relative yield loss was non-linear, though for the most resistant genotype Framida only the linear part of the relation was obtained, as even at high infestation levels only moderate infection levels were achieved. The results suggest that for resistant genotypes, tolerance can best be quantified as a reduced relative yield loss per aboveground Striga plant, whereas for less resistant genotypes the maximum relative yield loss can best be used. Whether both expressions of tolerance are interrelated could not be resolved. Complications of screening for tolerance under field conditions are discussed

Mode analysis in optics through fractional transforms

The relationship between the mode content and the fractional Fourier and fractional Hankel transforms of a function is established. It is shown that the Laguerre-Gauss spectrum of a rotationally symmetric wave front can be determined from the wave front's fractional Hankel transforms taken at the optical axis

Orthonormal mode sets for the two-dimensional fractional Fourier transformation

A family of orthonormal mode sets arises when Hermite-Gauss modes propagate through lossless first-order optical systems. It is shown that the modes at the output of the system are eigenfunctions for the symmetric fractional Fourier transformation if and only if the system is described by an orthosymplectic ray transformation matrix. Essentially new orthonormal mode sets can be obtained by letting helical Laguerre-Gauss modes propagate through an antisymmetric fractional Fourier transformer. The properties of these modes and their representation on the orbital Poincare sphere are studied